Heights in diophantine geometry

Author(s)

Bibliographic Information

Heights in diophantine geometry

Enrico Bombieri, Walter Gubler

(New mathematical monographs, 4)

Cambridge University Press, 2006

  • : hardback
  • : pbk.

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Note

Includes bibliographical references (p. 620-634) and index

Description and Table of Contents

Description

Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and give a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time. The book concludes with a comprehensive bibliography. It is destined to be a definitive reference on modern diophantine geometry, bringing a new standard of rigor and elegance to the field.

Table of Contents

  • 1. Heights
  • 2. Weil heights
  • 3. Linear tori
  • 4. Small points
  • 5. The unit equation
  • 6. Roth's theorem
  • 7. The subspace theorem
  • 8. Abelian varieties
  • 9. Neron-Tate heights
  • 10. The Mordell-Weil theorem
  • 11. Faltings theorem
  • 12. The ABC-conjecture
  • 13. Nevanlinna theory
  • 14. The Vojta conjectures
  • Appendix A. Algebraic geometry
  • Appendix B. Ramification
  • Appendix C. Geometry of numbers
  • Bibliography
  • Glossary of notation
  • Index.

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Details

  • NCID
    BA75127415
  • ISBN
    • 9780521846158
    • 9780521712293
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge, UK
  • Pages/Volumes
    xvi, 652 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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